Mokonyane wanted the companies to prove the sincerity of their apology by contributing money towards the building of a R1 billion children's hospital to honour former president Nelson Mandela, the newspaper reported.
She reportedly revealed at a fundraiser in Johannesburg on Tuesday that she had met three of the companies to ask them to make a meaningful contribution.
"These guys have got our money in their pockets. Let's call them and say: 'Guys, you can't just make a public apology. Go build the Nelson Mandela Children's Hospital," she was quoted as saying.
According to The Sowetan, the companies had promised to get back to her with their decisions.
A R1.4bn fine was recently imposed on 15 companies by the Competition Commission for collusion in the construction industry.